Three dimensional modulation-enhanced single-molecule localization techniques, such as ModLoc, offer advancements in axial localization precision across the entire field of view and axial capture range, by applying phase shifting to the illumination pattern. However, this improvement is limited by the pitch of the illumination pattern that can be used and requires registration between separate regions of the camera. To overcome these limitations, we present ZIMFLUX, a method that combines astigmatic point-spread-function (PSF) engineering with a structured illumination pattern in all three spatial dimensions. In order to achieve this we address challenges such as optical aberrations, refractive index mismatch, supercritical angle fluorescence (SAF), and imaging at varying depths within a sample, by implementing a vectorial PSF model. In scenarios involving refractive index mismatch between the sample and immersion medium, the astigmatic PSF loses its ellipticity at greater imaging depths, leading to a deterioration in axial localization precision. In contrast, our simulations demonstrate that ZIMFLUX maintains high axial localization precision even when imaging deeper into the sample. Experimental results show unbiased localization of 3D 80 nm DNA-origami nanostructures in SAF conditions with a 1.5-fold improvement in axial localization precision when comparing ZIMFLUX to conventional SMLM methods that rely solely on astigmatic PSF engineering.

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To better understand the interactions between biological molecules, a high optical resolution in all three dimensions is crucial. The intrinsically lower axial resolution of microscopes however, is a limiting factor in fluorescence imaging, correspondingly in fluorescence based single molecule localization microscopy (SMLM). Here, we present a method to improve the axial localization precision in SMLM by combining point-spread-function engineering with total internal reflection fluorescence (TIRF) fields with decay lengths that vary within the on-time of a fluorophore. Such time-varying illumination field intensity allows one to extract additional axial location information from the emitted photons. With this time varying illumination approach, we show that axial localization is improved two-fold over TIRF-based SMLM using astigmatic PSFs. We calculate theoretical resolution gains for various imaging conditions via the Cramér Rao Lower Bound (CRLB), a commonly used metric to compute the best attainable localization precision in SMLM.

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Single-molecule localization microscopy requires sparse activation of emitters to circumvent the diffraction limit. In densely labeled or thick samples, overlap of emitter images is inevitable. Single-molecule localization of these samples results in a biased parameter estimate with a wrong model of the number of emitters. On the other hand, multiple emitter fitting suffers from point spread function degeneracy, which increases model and parameter uncertainty. To better estimate the model, parameters and uncertainties, a three-dimensional Bayesian multiple emitter fitting algorithm was constructed using Reversible Jump Markov Chain Monte Carlo. It reconstructs the posterior density of both the model and the parameters, namely the three-dimensional position and photon intensity, of overlapping emitters. The ability of the algorithm to separate two emitters at varying distance was evaluated using an astigmatic point spread function. We found that for astigmatic imaging, the posterior distribution of the emitter positions is multimodal when emitters are within two times the in-focus standard deviation of the point spread function. This multimodality describes the ambiguity in position that astigmatism introduces in localization microscopy. Biplane imaging was also tested, proving capable of separating emitters up to 0.75 times the in-focus standard deviation of the point spread function while staying free of multimodality. The posteriors seen in astigmatic and biplane imaging demonstrate how the algorithm can identify point spread function degeneracy and evaluate imaging techniques for three-dimensional multiple-emitter fitting performance.

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Single Molecule Localization Microscopy (SMLM) has enabled researchers to breakthrough the diffraction limit and obtain nanometer resolution images of macromolecular structures. But due to the time involved in obtaining ample data for proper image, the technique is venerable to many problem including fluctuations due to thermal gradients from surrounding which cause the frames to drift. SMLM relies on the stochastic blinking of fluorophore probes. Thus drift in SMLM could be explicitly modelled as a stochastic state space process. These models could be used to perform drift correction. Two state space models are proposed relying on different properties of SMLM.

The first model utilizes shifting of underlying image structure. The state space model for this property is constructed using shift matrices. A system identification method along with image reconstruction method is also derived to form the drift compensation algorithm for this model. This algorithm is further developed to provide adequate performance within low computational time. The second model relies on the position of emitter molecules and utilizes linking or pairing of fluorophore probes in succeeding frame to obtain the output data. Drift compensation algorithm for this model is constructed using Prediction Error Methods (PEM) and Kalman (RTS) smoother. The drift correction algorithm for these two models are also bench-marked with existing algorithms to obtain insight into performance. Furthermore, other properties of these algorithms are explored using simulation dataset and recommendation are provided for improvement and further research.

High-NA light sheet illumination can improve the resolution of single-molecule localization microscopy (SMLM) by reducing the background fluorescence. These approaches currently require custom-made sample holders or additional specialized objectives, which makes the sample mounting or the optical system complex and therefore reduces the usability of these approaches. Here, we developed a single-objective lens-inclined light sheet microscope (SOLEIL) that is capable of 2D and 3D SMLM in thick samples. SOLEIL combines oblique illumination with point spread function PSF engineering to enable dSTORM imaging in a wide variety of samples. SOLEIL is compatible with standard sample holders and off-the-shelve optics and standard high NA objectives. To accomplish optimal optical sectioning we show that there is an ideal oblique angle and sheet thickness. Furthermore, to show what optical sectioning delivers for SMLM we benchmark SOLEIL against widefield and HILO microscopy with several biological samples. SOLEIL delivers in 15 μm thick Caco2-BBE cells a 374% higher intensity to background ratio and a 54% improvement in the estimated CRLB compared to widefield illumination, and a 184% higher intensity to background ratio and a 20% improvement in the estimated CRLB compared to HILO illumination.

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The microscope is an essential tool for biologists. Since the late 16th century, it has given researchers a better understanding of cell processes and greatly advanced healthcare. In this century, Single molecule localization microscopy (SMLM) has revolutionized optical microscopy by breaking the optical diffraction limit. Sparsely activating emitters in a sample labeled with fluorophores, the object can be reconstructed by estimating their positions using the system point spread function (PSF). These localization algorithms are the state of the art
in optical imaging, using unbiased estimators to reach the theoretical minimum uncertainty, or Cramér-Rao lower bound (CRLB).
While SMLM works well when emitters are sparsely activated, overlap of the emitter images is inevitable for thick or densely labeled samples. When SMLM is used on such images, the estimates become biased and the algorithm cannot find the correct number of emitters. Most techniques also make a deterministic estimate and are incapable of representing the uncertainty of estimates for dense samples.
A three-dimensional, Bayesian multiple emitter fitting algorithm is constructed using reversible jump Markov chain Monte Carlo (RJMCMC). While following the structure of Bayesian multiple-emitter fitting (BAMF), novel RJMCMC moves are designed to sample the parameters. The algorithm also jumps through models, estimating the number of emitters. It asymptotically samples from the posterior, revealing uncertainties in three-dimensional imaging that other techniques are incapable of imaging.
The algorithm was tested with astigmatic and biplane imaging. It has proven capable of consistently finding the correct model when a prior on emitter intensity is used. When separating two emitters, posterior density reconstruction revealed non-Gaussian emitter position uncertainties. Upon further investigation, the posterior density was found to be multimodal, with
both modes representative of the data and indistinguishable in terms of likelihood. This shows the algorithm can quantify three-dimensional PSF degeneracy and can become a vital tool for researchers to analyze their imaging setup. We also expect it to be especially effective when combined with modulation-enhanced localization microscopy (meLM) techniques.

Modulation enhanced single-molecule localization microscopy (meSMLM) methods improve the localization precision by using patterned illumination to encode additional position information. Iterative meSMLM (imeSMLM) methods iteratively generate prior information on emitter positions, used to locally improve the localization precision during subsequent iterations. The Cramér-Rao lower bound cannot incorporate prior information to bound the best achievable localization precision because it requires estimators to be unbiased. By treating estimands as random variables with a known prior distribution, the Van Trees inequality (VTI) can be used to bound the best possible localization precision of imeSMLM methods. An imeSMLM method is considered, where the positions of in-plane standing-wave illumination patterns are controlled over the course of multiple iterations. Using the VTI, we analytically approximate a lower bound on the maximum localization precision of imeSMLM methods that make use of standing-wave illumination patterns. In addition, we evaluate the maximally achievable localization precision for different illumination pattern placement strategies using Monte Carlo simulations. We show that in the absence of background and under perfect modulation, the information content of signal photons increases exponentially as a function of the iteration count. However, the information increase is no longer exponential as a function of the iteration count under non-zero background, imperfect modulation, or limited mechanical resolution of the illumination positioning system. As a result, imeSMLM with two iterations reaches at most a fivefold improvement over SMLM at 8 expected background photons per pixel and 95% modulation contrast. Moreover, the information increase from imeSMLM is balanced by a reduced signal photon rate. Therefore, SMLM outperforms imeSMLM when considering an equal measurement time and illumination power per iteration. Finally, the VTI is an excellent tool for the assessment of the performance of illumination control and is therefore the method of choice for optimal design and control of imeSMLM methods.

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Localization microscopy offers resolutions down to a single nanometer but currently requires additional dedicated hardware or fiducial markers to reduce resolution loss from the drift of the sample. Drift estimation without fiducial markers is typically implemented using redundant cross correlation (RCC). We show that RCC has sub-optimal precision and bias, which leaves room for improvement. Here, we minimize a bound on the entropy of the obtained localizations to efficiently compute a precise drift estimate. Within practical compute-time constraints, simulations show a 5x improvement in drift estimation precision over the widely used RCC algorithm. The algorithm operates directly on fluorophore localizations and is tested on simulated and experimental datasets in 2D and 3D. An open source implementation is provided, implemented in Python and C++, and can utilize a GPU if available.

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Accurate image alignment is critical in multicolor single-molecule fluorescence microscopy. Global alignment using affine transformations leaves residual errors due to the nonlinearity of the distortions, which decreases the effective field of view. Subsequent local refinement demands either large amounts of reference data and processing time or specialized imaging techniques like active stabilization. Here, we present a global alignment method, S/T polynomial decomposition, that uses sums of Zernike polynomial gradients to decompose the distortion between two images, correcting both linear and nonlinear distortions simultaneously. With minimal reference data, we gain diagnostic information about the distortion and achieve a colocalization accuracy comparable to local registration methods across the entire field of view. @en

For a long time, scientists believed that it is not possible to achieve a better microscopic resolution than half the wavelength of light (~ 200 nm). During the last decades, various super-resolution fluorescence microscopy techniques have been developed, offering high-resolution imaging beyond the diffraction limit. It has been established as one of the major tools currently available for the study and analysis of biological tissues. The observation of, previously limited and unclear, cellular structures has demonstrated the great promise of super-resolution fluorescence microscopy in exemplifying biological processes at the cellular level. Inherently, single-molecule localization microscopy (SMLM) is based upon acquiring a sequence of diffraction-limited images, consisting of localizations of sparsely distributed emitting fluorophores. Next, precise and accurate estimates of the spatial coordinates of the fluorophores, placed on the structures of interest, are made. Subsequently, all recovered emitter positions from each frame are combined, and a super-resolution image is generated. One of the most crucial questions in SMLM concerns the precision with which the location of a single molecule can be determined. The Cramér–Rao lower bound (CRLB) is used to quantify the estimation performance in terms of localization precision. Recently, several modulation enhanced methods have shown resolution improvement by combining structured patterned illumination with SMLM techniques, such as MINFLUX and SIMFLUX. However, the analysis of images by SMLM and these modulation enhanced methods requires sparse activation regions to prevent overlap between active emitters. Recently, several methods have been developed with the ability to analyze higher density data, allowing partial overlap between emitters. In this work, we propose a maximum likelihood-based, modulation enhanced SMLM method able to localize multiple active emitters within a single region of interest (ROI), which we refer to as Multi- SIMFLUX. The mathematical framework of the algorithm is comprehensively built up throughout this work. The performance of the algorithm has been evaluated, and validated under a wide range of realistic imaging conditions. This involves various active-emitter densities, different emitter- and background intensities, numerous emitter configurations, a multitude of ROI-sizes and point spread function widths. As theoretically expected, our approach significantly outperforms conventional 2DGaussian SMLM with a twofold improvement factor in terms of localization precision for various emitter densities and intensities. At higher active emitter imaging densities, the extension from a single to a multi-emitter approach showed a clear improvement in recall fraction.

MINFLUX offers a breakthrough in single molecule localization precision, but is limited in field of view. Here we combine centroid estimation and illumination pattern induced photon count variations in a conventional widefield imaging setup to extract position information over a typical micrometer-sized field of view. We show a near two-fold improvement in precision over standard localization with the same photon count on DNA-origami nanostructures and tubulin in cells, using DNA-PAINT and STORM imaging.

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Super Resolution Microscopy is a technique to image objects with resolution higher than the diffraction limit, the fundamental limit to the resolution of a microscope. One of the techniques used for Super Resolution Microscopy is Single Molecule Localization Microscopy (SMLM). For this method, a sample is labeled using fluorophores (fluorescent proteins or dyes), and each individual fluorophore is imaged individually. The fluorophores can be localized with a precision much higher than the diffraction limit, since the localization precision is only limited by the amount of photons collected. By combining the localizations of all the fluorophores, the complete object can be reconstructed with resolution higher than the diffraction limit. To achieve a high localization precision, a model for the Point Spread Function (PSF) of the microscope is required. The PSF describes how the microscope distorts the image of the fluorophore. This model is used to estimate the fluorophore location in the sample. This means the model needs to be very accurate and unbiased. Furthermore, because an experiment contains hundred of thousands of images and the model needs to be evaluated multiple times per localization, the model also needs to be fast to evaluate. Traditional fitters model the PSF with a Gaussian approximation. However, more recent studies showed the errors introduced by this approximation. More accurate models have been introduced, such as C-Spline based approximations. These C-Splines require over a million spline coefficients, and therefore lots of calibration data. In this research, it is investigated if Simplex B-Splines can be used to better approximate the PSF. Simplex B-Splines consist of multiple B-Splines defined on a triangulation of simplices. This allows for a very flexible model structure and high accuracy using a relatively low number of parameters. Most applications assume the PSF is constant over the field of view. However, due to varying aberrations or refractive index mismatches the PSF actually changes with the fluorophore position in the field of view. If these changes in the PSF are not corrected for, the precision is reduced or a significant bias is introduced. B-splines allow the model to be extended to higher dimensions, and can therefore also model these changes to the PSF. Different metrics are used to compare models. Using a statistical (chi squared) test the model quality can be assessed. Localization precision is verified by implementing the model in a MLE algorithm, and by showing that the standard deviation reaches the theoretical lower bound for precision, the CRLB.
In this research it is shown that the performance of B-Spline models is comparable to state-of-the-art methods, but uses 144 times fewer spline coefficients. Furthermore, the B-Splines were also successfully extended to higher dimensions, to reduce the effect of a varying PSF.